# Comparative Efficiency and Sensitivity Analysis of AC and DC Power Distribution Paradigms for Residential Localities

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## Abstract

**:**

## 1. Introduction

#### Innovative Aspects of the Current Research Effort

## 2. Modeling of the Systems

#### 2.1. Distribution of Load Using Normal Distribution for Non-Fixed Category of Load

#### 2.1.1. Off Load Method

_{1}is given as:

_{Li}(t

_{1}) represents the averaged value at t

_{1}, ${x}_{Li}({t}_{1})$ represents the power consumption, ${x}_{min-i}$ represents the minimum power consumption of and ${x}_{min-i}$ represents instantaneous maximum power consumption of the i

^{th}load.

^{th}load is at ON sate while m represents the total number of buildings against each SST and b

_{i}represents the number of BBs in which i

^{th}load is at OFF state.

#### 2.1.2. On/Off Method for Fixed Category Load

_{1}’ is presented in (4).

_{F-i}(t

_{1}) denotes the power t

_{1}and ${x}_{Fmax-i}$ represents the rated value of the i

^{th}load.

^{th}load for ‘m’ number of BBs against each SST can be calculated using (5):

^{th}load for all BBs.

^{th}load is ON can be represented as (6):

#### 2.2. Mathematical Modeling

_{1}” are taken from [57], which is the effort of two of current authors.

#### 2.2.1. DC System

^{th}building), the input power p

_{j}(t

_{1}) may be calculated as the total sum of all four types of load categories at time t

_{1}, as shown in (7)

_{1}; ${p}_{Dijk-in}\left({t}_{1}\right)$, ${p}_{Aijk-in}\left({t}_{1}\right)$, ${p}_{Iijk-in}\left({t}_{1}\right)$ and ${p}_{VSDijk-in}\left({t}_{1}\right)$ are the ith DC, AC, independent and VSD input powers in jth building block of kth SST, respectively. Normalized load data obtained by the process explained in Section 2.1 is used for the loads in Equation (1) with realistic load ratings from manufacturer’s data (given in Table 3). The appliance rating load matrix for DC loads is presented as:

_{1}and ${\lambda}_{SD-j}$ is the associated DC–DC conversion loss. ${\alpha}_{j},{\beta}_{j},{\gamma}_{j},{\delta}_{j},{\epsilon}_{j}$ are the co-efficiencies obtained through curve fitting tool. ${\lambda}_{SD-j}$ is assumed to be constant for different power generation because this loss has negligible effect on system efficiency. It is also assumed that each building has same PV generation capacity; hence, the equation for PV system in all BBs is same. Subsequently, the input power drawn (or output power supplied in case of excess generation) by the system SST can be evaluated from (11):

_{1}, which is calculated by summing the input power of each SST.${\eta}_{DCSystem}\left({t}_{1}\right)$ is the efficiency of DC system, which is calculated by the dividing the sum of grid power ${p}_{DG}\left({t}_{1}\right)$ and the total solar power ${p}_{solar-total}\left({t}_{1}\right)$ to the total load power ${p}_{Load-total}\left({t}_{1}\right)$ at time t

_{1}, and ${p}_{Load-total}\left({t}_{1}\right)$ is the total load power obtained by the summation of the power of each load category present in each building of each SST at time t

_{1}.

#### 2.2.2. AC System

^{th}XMFR, respectively. Similar procedure is performed for rating and efficiency matrices in AC system using curve fitting tool.

^{th}building. Similar to the case of DC, ${\lambda}_{SA-j}$ is assumed constant. The consideration of the reactive component is presented in (15).

_{SA}variable, which represents solar to AC power conversion.

_{in-XMFR}, can be evaluated using (16):

_{1}

_{1}.

_{rms}AC) is chosen, which draws its support from [33].

#### 2.3. Sensitivity Analysis

#### 2.3.1. PV Capacity Variation

_{solar−j}for jth building is given in (18):

^{th}BB. The installed capacity is varied to see the effect of PV capacity on overall system efficiency. For this purpose, Cs is considered 1pu (normalized form), and variable ‘x’ is taken as scaling factor for capacity; thereby, (18) takes the form of (19) and (20).

#### 2.3.2. PEC Efficiency Variation

_{1}from its original value.

## 3. Main Results

#### 3.1. Structural Visualization of Scenarios in Both Systems

#### 3.2. Comparative Efficiency Analysis of Both Systems

#### 3.3. Comparative Sensitivity Analysis on Both Systems

#### 3.4. Discussion

## 4. Conclusions and Future Recommendations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Power Electronic Converter | PEC |

High Voltage Direct Current | HVDC |

Brushless Direct Current | BLDC |

Variable Speed Drive | VSD |

Electric Power Research Institute | EPRI |

Building Block | BB |

Transformer | XFMR |

Solid State Transformer | SST |

time | t |

Input Power | P_{i} |

AC Load | A |

DC Load | D |

Independent Load | I |

Efficiency | $\eta $ |

Standard Deviation | SD |

Loss Factor | $\lambda $ |

DC to DC | dd |

AC to DC | ad |

DC to AC | da |

Reactive Power | q |

Active Power | p |

Load | l |

Inverter loss-installed at solar | SA |

Coefficients of curve fitting tool equation | ${\alpha}_{j},{\beta}_{j},{\gamma}_{j},{\delta}_{j},{\epsilon}_{j}$ |

Output | out |

Input | in |

## Appendix A. Sensitivity Analysis Curves of AC and DC Distribution Systems

**Figure A1.**(

**A**) AC–DC Converter Efficiency Variation in AC System (Weekdays); (

**B**) AC–DC Converter Efficiency Variation in AC System (Weekends).

**Figure A2.**(

**A**) VSD Converter Efficiency Variation in AC Systems (Weekdays); (

**B**) VSD Converter Efficiency Variation in AC Systems (Weekends).

**Figure A3.**(

**A**) PV Capacity Variation in AC Systems (Weekdays); (

**B**) PV Capacity Variation in AC Systems (Weekends).

**Figure A4.**(

**A**) DC–DC Converter Efficiency in DC System (Weekdays); (

**B**) DC–DC Converter Efficiency in DC System (Weekends).

**Figure A5.**(

**A**) DC–AC Converter Efficiency Variation in DC System (Weekdays); (

**B**) DC–AC Converter Efficiency Variation in DC System (Weekends).

**Figure A6.**(

**A**) VSD Converter Efficiency Variation in DC System (Weekdays); (

**B**) VSD Converter Efficiency Variation in DC System (Weekends).

**Figure A7.**(

**A**) PV Capacity Variation in DC System (Weekdays); (

**B**) PV Capacity Variation in DC System (Weekends).

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**Figure 1.**(

**a**) Air conditioner load profile (November); (

**b**) Distribution data with standard deviation of 33.

**Table 1.**Summarized form of various research efforts mentioning around a dozen points of comparison in the approaches of various research efforts.

Research Work | Load Modelling | Multiple Voltage Levels | Load Variation with Respect to Time | Conductor/Cable Losses | Energy Storage (Battery) | Renewable Energy Resources (PV System) | Analysis on Partial Loading | Perform for Residential/Commercial | Comparison with AC System | PEC Efficiency Variation | PV Capacity Variation | Result |
---|---|---|---|---|---|---|---|---|---|---|---|---|

[30] | - | - | - | ✔ | - | - | - | Commercial | ✔ | - | - | AC is better than DC. The study is performed on low and medium voltage networks |

[29] | ✔ | - | - | - | - | ✔ | - | Residential | ✔ | - | - | DC is better. The study is performed with fixed PEC efficiency |

[35] | ✔ | - | ✔ | - | - | - | ✔ | Residential | - | ✔ | - | DC is feasible. Loss comparison is performed allowing load variation. |

[18] | ✔ | - | - | ✔ | ✔ | ✔ | ✔ | Residential | ✔ | ✔ | - | DC is feasible up to some extent. The authors proposed almost equal efficiency for AC and DC at low voltage distribution scale. |

[38] | - | - | ✔ | - | ✔ | ✔ | ✔ | Residential | ✔ | ✔ | - | DC is better. The study is performed by considering all loads as DC without considering PEC efficiency variation |

[25] | - | - | ✔ | - | ✔ | ✔ | ✔ | Residential | ✔ | - | - | DC is better. The study is performed by considering and PEC efficiency variation |

[33] | ✔ | - | ✔ | - | - | - | - | Residential | ✔ | ✔ | - | AC and DC are comparable. Efficiency of PECs is varied in fix range. |

[24] | - | - | - | - | - | - | - | Residential | ✔ | - | - | DC is better. Limited loads selection and fixed PEC efficiency |

[23] | - | - | ✔ | - | - | ✔ | - | Residential | ✔ | - | - | AC is better. Load variation is considered, however, the effect of load variation on PEC efficiency is not considered |

[27] | - | ✔ | ✔ | - | - | ✔ | - | Commercial | ✔ | - | - | DC is better. Hardware based analysis is performed with limited loads |

[19] | - | - | ✔ | - | - | ✔ | - | Commercial | ✔ | - | - | DC is better. Seasonal effect is considered, however, certain basic parameters related to load and PEC are missing. |

[26] | - | - | - | ✔ | - | ✔ | - | Commercial | ✔ | - | - | DC is better. A total of 230 V AC is compared against 380 V Dc with limited scenarios and loads. |

[21] | ✔ | ✔ | - | - | - | - | - | Residential | ✔ | - | - | DC is feasible. Limited scenario with constant loads and fixed PEC efficiency |

[34] | ✔ | - | ✔ | ✔ | - | ✔ | - | Residential | ✔ | ✔ | ✔ | DC is better. Time based study is performed with averaged load models, the loads are categorized according to the power demand |

[22] | - | ✔ | - | ✔ | - | ✔ | - | Residential | ✔ | - | - | DC shows better efficiency at different voltage levels. The comparative analysis is performed on the basis of voltage levels. |

[13] | ✔ | ✔ | - | - | - | - | - | Residential/Commercial | - | - | - | DC shows better energy savings with DC loads. The comparison is performed with futuristic approach, by considering DC loads only. |

[20] | ✔ | - | ✔ | ✔ | ✔ | ✔ | ✔ | Commercial | ✔ | - | ✔ | DC shows better efficiency about 9.9% in base case while 17.9% in best case. |

[23] | - | - | ✔ | - | - | ✔ | - | Residential | ✔ | - | - | AC shows better efficiency as compared to DC |

[28] | - | ✔ | ✔ | ✔ | ✔ | ✔ | - | Commercial | ✔ | - | - | Efficiency of AC and DC is comparable and depend upon voltage level of DC mainly. |

[31] | - | ✔ | ✔ | ✔ | - | - | - | Distribution level | ✔ | - | - | With DC is more efficient regarding energy losses, voltage profiles than its AC counterpart |

[32] | ✔ | - | ✔ | - | - | ✔ | - | Residential | ✔ | ✔ | ✔ | AC System shows better efficiency during the presence of PV solar system |

[37] | ✔ | - | ✔ | - | - | - | - | Residential | ✔ | - | - | DC shows better efficiency with separate and bulk PEC topologies. |

Serial No. | Category | Energy Used (Quad. Btu) | Energy Usage Converted to % |
---|---|---|---|

1 | Space Heating | 0.42 | 8.8 |

2 | Water Heating | 0.48 | 10 |

3 | Space Cooling | 1.02 | 21.3 |

4 | Lighting | 0.53 | 11.1 |

5 | Refrigeration | 0.45 | 9.4 |

6 | Electronics | 0.33 | 6.9 |

7 | Wet Cleaning | 0.33 | 6.9 |

8 | Cooking | 0.11 | 2.3 |

9 | Computers | 0.19 | 4 |

10 | Other | 0.94 | 19.6 |

Serial No. | Appliances | Load Ratings (W) | Category | Load Type |
---|---|---|---|---|

1 | Indoor Lights | 13 W per light | Fixed | D |

2 | Television | 120–130 | Fixed | D |

3 | Computer | 4–250 | Non-Fixed | D |

4 | Dishwasher | 1200–1500 | Fixed | A |

5 | Clothe Dryer | 1000–4000 | Non-Fixed | A |

6 | Clothe Washer | 500 | Fixed | A |

7 | Air Conditioner | 1000–6000 | Non-Fixed | VSD |

8 | Refrigerator | 100–220 | Non-Fixed | VSD |

9 | Cooking Equip. | 2150 | Fixed | I |

10 | Water Heater | 3000 | Fixed | I |

11 | Space Heater | 2000–3000 | Fixed | I |

Serial No. | Appliances | Category | Required PEC Ratings (Maximum) | PEC for DC System | PEC for AC System |
---|---|---|---|---|---|

1 | Indoor Lights | D | 300 W | DC/DC | AC/DC |

2 | Television | D | 150 W | DC/DC | AC/DC |

3 | Computer | D | 300 W | DC/DC | AC/DC |

4 | Dishwasher | A | 1700 W | DC/AC | N/A |

5 | Clothe Dryer | A | 5000 W | DC/AC | N/A |

6 | Clothe Washer | A | 600 W | DC/AC | N/A |

7 | Air Conditioner | VSD | 8000 W | DC/AC | VSD |

8 | Refrigerator | VSD | 300 W | DC/AC | VSD |

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**MDPI and ACS Style**

Erteza Gelani, H.; Dastgeer, F.; Ali Shah, S.A.; Saeed, F.; Hassan Yousuf, M.; Afzal, H.M.W.; Bilal, A.; Chowdhury, M.S.; Techato, K.; Channumsin, S.;
et al. Comparative Efficiency and Sensitivity Analysis of AC and DC Power Distribution Paradigms for Residential Localities. *Sustainability* **2022**, *14*, 8220.
https://doi.org/10.3390/su14138220

**AMA Style**

Erteza Gelani H, Dastgeer F, Ali Shah SA, Saeed F, Hassan Yousuf M, Afzal HMW, Bilal A, Chowdhury MS, Techato K, Channumsin S,
et al. Comparative Efficiency and Sensitivity Analysis of AC and DC Power Distribution Paradigms for Residential Localities. *Sustainability*. 2022; 14(13):8220.
https://doi.org/10.3390/su14138220

**Chicago/Turabian Style**

Erteza Gelani, Hasan, Faizan Dastgeer, Sayyad Ahmad Ali Shah, Faisal Saeed, Muhammad Hassan Yousuf, Hafiz Muhammad Waqas Afzal, Abdullah Bilal, Md. Shahariar Chowdhury, Kuaanan Techato, Sittiporn Channumsin,
and et al. 2022. "Comparative Efficiency and Sensitivity Analysis of AC and DC Power Distribution Paradigms for Residential Localities" *Sustainability* 14, no. 13: 8220.
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